Problem

Source: JBMO Shortlist 2004

Tags: geometry, circumcircle, JBMO



Let ABC be a triangle inscribed in circle C. Circles C1,C2,C3 are tangent internally with circle C in A1,B1,C1 and tangent to sides [BC],[CA],[AB] in points A2,B2,C2 respectively, so that A,A1 are on one side of BC and so on. Lines A1A2,B1B2 and C1C2 intersect the circle C for second time at points A,B and C, respectively. If M=BBCC, prove that m(MAA)=90 .